Mubarak temporarily delegated presidential power to Ahmed Nazif, the country's prime minister, the television said.
"He has issued a presidential decree delegating Ahmed Nazif presidential powers until he returns," it said.
The health of Mubarak, who turns 82 this year, is usually a taboo subject in the country he has ruled since 1981, fuelling regular rumours on the subject.
Samer Shehata, an Egyptian professor at Georgetown University, told Al Jazeera the fact that Egypt has no vice-president, news of Mubarak's undergoing surgery becomes "a concern to many Egyptians and many outside the country if it does not go well".
"Whenever there is a health issue with [the] president, all of a sudden questions of succession rise to the forefront of Egyptian politics, tremendous speculation, some concern and anxiety, and this is just one of those examples," he said.
"The succession issue is one of the most hotly contested issues in Egypt right now. For good reason, it's tied into the issue of democratization and reform and so on."
In 2007, rumours about Mubarak's poor health were rife to the extent that the president was forced to make an unscheduled public appearance to dispel them.
One year later, Ibrahim Eissa, the editor-in-chief of the independent daily al-Dustur, was sentenced to two months in jail after his newspaper published rumours on Mubarak's health. He later received a presidential pardon.
Mubarak's fifth six-year term as president will end in 2011 and press reports in Egypt have suggested that his son Gamal is likely to succeed him.
Neither Mubarak nor his son has made any clear statement on the matter.
However, Mubarak said on Thursday that Mohamed ElBaradei, former head of the International Atomic Energy Agency (IAEA), could run for the presidency provided he respected the constitution.
ElBaradei, 67, last month flew to Cairo, the capital, to a rapturous welcome from supporters and formed the National Association for Change.
He has said he will run for president on condition that the constitution is amended.
Under Egyptian law, a presidential candidate is required to have been a leading member of a party for at least one year and for the party to have existed for at least five years.